1 Background

This study tried to examine the effects of change attitudes of HR department (University of Tehran) on organizational innovation and happiness. The total population of the present study was 348 employees (HR departments) of the University of Tehran. 219 (62.9%) of the respondents were male and 129 (37.1%) were female. We also know about their duration of employment or work experience in years (experience).

The questionnaire items use a 5-level Likert scale from 1 to 5 (strongly disagree = 1, disagree = 2, have no opinion = 3, agree = 4 and strongly agree = 5).

Independent variables:

Dependent variables

Moreover, the questionnaire on organizational happiness suggests that if the staff think of their workplace as a learning environment in which they can positively participate in a meaningful interesting job, organizational happiness will take place.

2 Setup

library(tidyverse)
## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.1 ──
## ✓ ggplot2 3.3.5     ✓ purrr   0.3.4
## ✓ tibble  3.1.6     ✓ dplyr   1.0.8
## ✓ tidyr   1.2.0     ✓ stringr 1.4.0
## ✓ readr   2.1.2     ✓ forcats 0.5.1
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## x dplyr::filter() masks stats::filter()
## x dplyr::lag()    masks stats::lag()
library(summarytools) # dfSummary(), descr(), freq()
## 
## Attaching package: 'summarytools'
## The following object is masked from 'package:tibble':
## 
##     view
library(psych)
## 
## Attaching package: 'psych'
## The following objects are masked from 'package:ggplot2':
## 
##     %+%, alpha
library(performance)

# packages with additional graphics options
library(car)
## Loading required package: carData
## 
## Attaching package: 'car'
## The following object is masked from 'package:psych':
## 
##     logit
## The following object is masked from 'package:dplyr':
## 
##     recode
## The following object is masked from 'package:purrr':
## 
##     some
library(GGally)
## Registered S3 method overwritten by 'GGally':
##   method from   
##   +.gg   ggplot2
library(cowplot)

3 Read the data

data <- read_csv("students/data/Keshavarz_1_HR.csv")
## Rows: 348 Columns: 51
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (51): Gender, experience, q01, q02, q03, q04, q05, q06, q07, q08, q09, q...
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
spec(data)
## cols(
##   Gender = col_double(),
##   experience = col_double(),
##   q01 = col_double(),
##   q02 = col_double(),
##   q03 = col_double(),
##   q04 = col_double(),
##   q05 = col_double(),
##   q06 = col_double(),
##   q07 = col_double(),
##   q08 = col_double(),
##   q09 = col_double(),
##   q10 = col_double(),
##   q11 = col_double(),
##   q12 = col_double(),
##   q13 = col_double(),
##   q14 = col_double(),
##   q15 = col_double(),
##   q16 = col_double(),
##   q17 = col_double(),
##   q18 = col_double(),
##   q19 = col_double(),
##   q20 = col_double(),
##   q21 = col_double(),
##   q22 = col_double(),
##   q23 = col_double(),
##   q24 = col_double(),
##   q25 = col_double(),
##   q26 = col_double(),
##   q27 = col_double(),
##   q28 = col_double(),
##   q29 = col_double(),
##   q30 = col_double(),
##   q31 = col_double(),
##   q32 = col_double(),
##   q33 = col_double(),
##   q34 = col_double(),
##   q35 = col_double(),
##   q36 = col_double(),
##   q37 = col_double(),
##   q38 = col_double(),
##   q39 = col_double(),
##   q40 = col_double(),
##   q41 = col_double(),
##   q42 = col_double(),
##   q43 = col_double(),
##   q44 = col_double(),
##   q45 = col_double(),
##   q46 = col_double(),
##   q47 = col_double(),
##   q48 = col_double(),
##   q49 = col_double()
## )
#view(dfSummary(data))
descr(data, stats="common")  
## Descriptive Statistics  
## data  
## N: 348  
## 
##                   experience   Gender      q01      q02      q03      q04      q05      q06      q07
## --------------- ------------ -------- -------- -------- -------- -------- -------- -------- --------
##            Mean         4.22     1.37     4.07     4.17     4.21     4.57     4.24     1.61     2.22
##         Std.Dev         1.23     0.48     1.14     1.13     1.18     0.83     1.00     0.72     1.10
##             Min         1.00     1.00     1.00     1.00     1.00     1.00     1.00     1.00     1.00
##          Median         4.00     1.00     4.00     5.00     5.00     5.00     4.50     1.00     2.00
##             Max         6.00     2.00     5.00     5.00     5.00     5.00     5.00     5.00     5.00
##         N.Valid       348.00   348.00   348.00   348.00   348.00   348.00   348.00   348.00   348.00
##       Pct.Valid       100.00   100.00   100.00   100.00   100.00   100.00   100.00   100.00   100.00
## 
## Table: Table continues below
## 
##  
## 
##                      q08      q09      q10      q11      q12      q13      q14      q15      q16
## --------------- -------- -------- -------- -------- -------- -------- -------- -------- --------
##            Mean     4.34     3.39     4.04     4.34     3.85     3.89     4.17     4.50     4.28
##         Std.Dev     0.99     1.03     0.97     0.85     1.08     1.06     1.05     0.74     0.92
##             Min     1.00     1.00     1.00     1.00     1.00     1.00     1.00     1.00     1.00
##          Median     5.00     3.00     4.00     5.00     4.00     4.00     4.00     5.00     5.00
##             Max     5.00     5.00     5.00     5.00     5.00     5.00     5.00     5.00     5.00
##         N.Valid   348.00   348.00   348.00   348.00   348.00   348.00   348.00   348.00   348.00
##       Pct.Valid   100.00   100.00   100.00   100.00   100.00   100.00   100.00   100.00   100.00
## 
## Table: Table continues below
## 
##  
## 
##                      q17      q18      q19      q20      q21      q22      q23      q24      q25
## --------------- -------- -------- -------- -------- -------- -------- -------- -------- --------
##            Mean     4.38     4.15     3.55     4.43     4.36     4.31     3.82     4.31     4.62
##         Std.Dev     0.75     0.94     0.90     0.84     0.84     0.79     0.89     0.75     0.65
##             Min     1.00     1.00     1.00     1.00     2.00     1.00     1.00     2.00     1.00
##          Median     5.00     4.00     3.00     5.00     5.00     4.00     4.00     4.00     5.00
##             Max     5.00     5.00     5.00     5.00     5.00     5.00     5.00     5.00     5.00
##         N.Valid   348.00   348.00   348.00   348.00   348.00   348.00   348.00   348.00   348.00
##       Pct.Valid   100.00   100.00   100.00   100.00   100.00   100.00   100.00   100.00   100.00
## 
## Table: Table continues below
## 
##  
## 
##                      q26      q27      q28      q29      q30      q31      q32      q33      q34
## --------------- -------- -------- -------- -------- -------- -------- -------- -------- --------
##            Mean     4.39     3.74     2.77     2.66     2.99     2.75     2.49     2.83     2.89
##         Std.Dev     0.80     1.20     1.08     1.18     1.21     1.30     1.11     1.06     1.03
##             Min     1.00     1.00     1.00     1.00     1.00     1.00     1.00     1.00     1.00
##          Median     5.00     4.00     3.00     3.00     3.00     3.00     2.00     3.00     3.00
##             Max     5.00     5.00     5.00     5.00     5.00     5.00     5.00     5.00     5.00
##         N.Valid   348.00   348.00   348.00   348.00   348.00   348.00   348.00   348.00   348.00
##       Pct.Valid   100.00   100.00   100.00   100.00   100.00   100.00   100.00   100.00   100.00
## 
## Table: Table continues below
## 
##  
## 
##                      q35      q36      q37      q38      q39      q40      q41      q42      q43
## --------------- -------- -------- -------- -------- -------- -------- -------- -------- --------
##            Mean     2.71     3.05     3.05     2.77     2.73     3.34     2.73     3.12     3.63
##         Std.Dev     1.24     1.13     1.06     1.10     1.18     1.06     1.17     1.11     1.04
##             Min     1.00     1.00     1.00     1.00     1.00     1.00     1.00     1.00     1.00
##          Median     2.50     3.00     3.00     2.00     3.00     3.00     2.00     3.00     4.00
##             Max     5.00     5.00     5.00     5.00     5.00     5.00     5.00     5.00     5.00
##         N.Valid   348.00   348.00   348.00   348.00   348.00   348.00   348.00   348.00   348.00
##       Pct.Valid   100.00   100.00   100.00   100.00   100.00   100.00   100.00   100.00   100.00
## 
## Table: Table continues below
## 
##  
## 
##                      q44      q45      q46      q47      q48      q49
## --------------- -------- -------- -------- -------- -------- --------
##            Mean     3.78     3.15     3.52     3.39     3.50     3.55
##         Std.Dev     0.91     1.12     1.04     0.99     0.88     0.97
##             Min     1.00     1.00     1.00     1.00     1.00     1.00
##          Median     4.00     3.00     4.00     4.00     4.00     4.00
##             Max     5.00     5.00     5.00     5.00     5.00     5.00
##         N.Valid   348.00   348.00   348.00   348.00   348.00   348.00
##       Pct.Valid   100.00   100.00   100.00   100.00   100.00   100.00
glimpse(data)
## Rows: 348
## Columns: 51
## $ Gender     <dbl> 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1,…
## $ experience <dbl> 5, 3, 3, 4, 6, 4, 2, 2, 3, 3, 4, 3, 3, 3, 3, 4, 5, 6, 3, 3,…
## $ q01        <dbl> 3, 1, 5, 5, 5, 3, 4, 4, 3, 5, 5, 5, 4, 5, 5, 2, 5, 4, 5, 5,…
## $ q02        <dbl> 5, 4, 5, 5, 5, 3, 4, 3, 4, 4, 4, 5, 5, 2, 2, 2, 5, 2, 5, 3,…
## $ q03        <dbl> 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 5, 5, 5, 4, 4, 4, 5, 2, 5, 3,…
## $ q04        <dbl> 5, 5, 5, 5, 5, 5, 5, 4, 4, 5, 5, 5, 5, 4, 4, 5, 5, 1, 4, 3,…
## $ q05        <dbl> 4, 4, 4, 5, 4, 1, 4, 5, 4, 5, 5, 4, 4, 4, 4, 2, 5, 4, 4, 3,…
## $ q06        <dbl> 2, 1, 1, 2, 1, 3, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 3, 3, 2,…
## $ q07        <dbl> 1, 1, 2, 1, 1, 4, 2, 4, 4, 4, 2, 2, 1, 4, 4, 2, 1, 1, 3, 2,…
## $ q08        <dbl> 5, 5, 5, 5, 5, 4, 3, 5, 5, 5, 5, 4, 3, 5, 5, 2, 5, 1, 4, 2,…
## $ q09        <dbl> 4, 5, 5, 3, 2, 4, 4, 5, 4, 4, 5, 1, 2, 4, 4, 2, 3, 2, 3, 2,…
## $ q10        <dbl> 4, 5, 4, 5, 5, 4, 5, 2, 4, 4, 5, 5, 4, 2, 4, 4, 5, 3, 4, 2,…
## $ q11        <dbl> 4, 5, 5, 5, 5, 5, 5, 4, 5, 4, 5, 5, 5, 4, 4, 4, 5, 4, 4, 2,…
## $ q12        <dbl> 4, 2, 5, 4, 4, 5, 4, 5, 4, 2, 5, 4, 4, 2, 4, 4, 5, 3, 4, 2,…
## $ q13        <dbl> 3, 5, 5, 4, 4, 1, 5, 4, 4, 4, 5, 4, 4, 2, 3, 2, 3, 1, 5, 3,…
## $ q14        <dbl> 4, 5, 4, 5, 5, 4, 5, 3, 4, 5, 5, 5, 3, 4, 5, 4, 5, 3, 5, 3,…
## $ q15        <dbl> 4, 5, 4, 5, 5, 5, 5, 4, 5, 5, 5, 5, 4, 4, 5, 4, 5, 5, 4, 2,…
## $ q16        <dbl> 4, 1, 5, 5, 5, 5, 4, 3, 4, 3, 5, 5, 4, 4, 5, 4, 5, 4, 4, 2,…
## $ q17        <dbl> 5, 5, 4, 5, 5, 5, 5, 2, 4, 4, 4, 4, 4, 5, 5, 4, 5, 3, 4, 2,…
## $ q18        <dbl> 5, 5, 4, 5, 5, 5, 5, 4, 4, 2, 5, 5, 4, 4, 5, 4, 5, 1, 5, 2,…
## $ q19        <dbl> 3, 5, 4, 4, 5, 3, 5, 3, 4, 3, 5, 5, 3, 3, 4, 4, 5, 3, 4, 2,…
## $ q20        <dbl> 4, 5, 5, 4, 5, 5, 5, 3, 5, 5, 4, 5, 4, 5, 5, 4, 5, 3, 4, 2,…
## $ q21        <dbl> 5, 5, 5, 5, 5, 4, 4, 3, 4, 3, 5, 5, 4, 5, 5, 4, 5, 4, 5, 2,…
## $ q22        <dbl> 5, 5, 4, 4, 5, 5, 4, 3, 4, 4, 5, 4, 4, 4, 5, 4, 5, 5, 5, 1,…
## $ q23        <dbl> 4, 5, 4, 5, 5, 5, 5, 5, 4, 5, 4, 5, 4, 4, 5, 4, 5, 4, 4, 2,…
## $ q24        <dbl> 4, 5, 5, 4, 5, 5, 4, 5, 4, 5, 4, 5, 4, 5, 5, 4, 5, 4, 4, 2,…
## $ q25        <dbl> 5, 5, 5, 5, 5, 2, 4, 5, 4, 5, 5, 5, 5, 5, 5, 4, 5, 4, 5, 2,…
## $ q26        <dbl> 4, 5, 4, 4, 5, 5, 4, 2, 5, 3, 4, 5, 4, 5, 5, 4, 3, 5, 1, 3,…
## $ q27        <dbl> 4, 4, 4, 3, 1, 3, 4, 3, 2, 4, 4, 4, 3, 2, 2, 4, 3, 3, 1, 4,…
## $ q28        <dbl> 4, 4, 4, 3, 2, 1, 3, 1, 1, 4, 3, 3, 2, 4, 5, 1, 1, 3, 2, 3,…
## $ q29        <dbl> 4, 4, 4, 1, 1, 1, 2, 1, 1, 4, 2, 3, 2, 4, 4, 2, 1, 4, 1, 3,…
## $ q30        <dbl> 4, 5, 4, 3, 1, 1, 1, 1, 2, 4, 3, 3, 2, 2, 2, 2, 1, 3, 3, 3,…
## $ q31        <dbl> 3, 4, 5, 4, 1, 1, 1, 2, 2, 2, 3, 3, 2, 2, 5, 2, 1, 1, 4, 3,…
## $ q32        <dbl> 5, 5, 4, 2, 2, 1, 1, 3, 2, 1, 4, 3, 1, 2, 5, 1, 1, 1, 2, 3,…
## $ q33        <dbl> 4, 4, 4, 3, 1, 2, 2, 3, 1, 4, 3, 3, 2, 4, 4, 1, 1, 3, 3, 2,…
## $ q34        <dbl> 3, 4, 4, 3, 4, 3, 1, 2, 2, 3, 2, 3, 2, 4, 4, 2, 1, 2, 4, 2,…
## $ q35        <dbl> 2, 3, 4, 1, 1, 1, 1, 1, 2, 1, 4, 3, 1, 2, 2, 2, 1, 4, 2, 3,…
## $ q36        <dbl> 4, 5, 4, 4, 1, 3, 1, 4, 2, 4, 3, 3, 1, 4, 4, 1, 1, 3, 3, 4,…
## $ q37        <dbl> 3, 4, 4, 3, 1, 1, 1, 3, 3, 4, 3, 3, 1, 5, 4, 2, 1, 3, 4, 3,…
## $ q38        <dbl> 3, 5, 4, 2, 1, 1, 1, 5, 2, 4, 3, 3, 2, 4, 4, 2, 1, 2, 4, 2,…
## $ q39        <dbl> 3, 3, 4, 4, 1, 3, 1, 4, 1, 1, 2, 3, 1, 1, 1, 2, 1, 3, 2, 2,…
## $ q40        <dbl> 4, 5, 2, 4, 2, 3, 2, 5, 4, 5, 2, 3, 4, 5, 5, 4, 3, 4, 4, 3,…
## $ q41        <dbl> 3, 4, 2, 4, 1, 1, 2, 1, 2, 4, 2, 3, 2, 1, 1, 2, 3, 3, 2, 3,…
## $ q42        <dbl> 3, 5, 5, 3, 1, 1, 1, 2, 4, 4, 3, 3, 1, 2, 4, 2, 3, 2, 2, 2,…
## $ q43        <dbl> 4, 5, 4, 4, 1, 3, 2, 4, 2, 5, 4, 3, 1, 5, 5, 1, 3, 3, 4, 2,…
## $ q44        <dbl> 5, 5, 4, 3, 1, 4, 2, 4, 4, 4, 4, 3, 4, 4, 5, 4, 4, 3, 2, 3,…
## $ q45        <dbl> 5, 5, 5, 4, 2, 3, 2, 4, 2, 2, 3, 3, 1, 4, 4, 4, 3, 4, 4, 4,…
## $ q46        <dbl> 4, 5, 5, 1, 1, 2, 4, 4, 2, 4, 4, 3, 2, 4, 4, 2, 3, 3, 3, 3,…
## $ q47        <dbl> 3, 5, 4, 1, 1, 1, 4, 2, 4, 4, 4, 3, 2, 2, 4, 2, 3, 4, 1, 3,…
## $ q48        <dbl> 4, 5, 5, 5, 2, 4, 4, 4, 4, 4, 3, 3, 4, 5, 5, 4, 3, 4, 4, 4,…
## $ q49        <dbl> 3, 5, 4, 4, 1, 1, 4, 2, 2, 4, 3, 3, 1, 2, 2, 2, 1, 2, 2, 3,…

4 Preprocessing

4.1 Basics

The analyses below show that items q06 and q07 correlate negatively with the scale. In “real life” they should be reversed during preprocessing. Removing comments in the next chunk will accomplish this.

dat <-
  data |> 
  mutate(Subj=as_factor(paste0("S", str_pad(1:348, width=3, side="left", pad="0"))),
         Gender = factor(Gender, levels=c(1,2), labels=c("male", "female")),
#        q06 = 6 - q06,
#        q07 = 6 - q07
         ) |> 
  relocate(Gender:experience, .after=Subj)

4.2 Scale statistics (Cronbach’s alpha)

You need to install.packages("psych") for good scale statistics and more.

4.2.1 Change attitude

  • alpha() computes Cronbach’s alpha and lots of other statistics
  • str(aocq) shows you exactly all the results computed by alpha()
  • with aocq$scores we extract the subjects’ scores (and can store them in dat)
aocq <- alpha(dat[, 1:18], check.keys=TRUE)
## Warning in alpha(dat[, 1:18], check.keys = TRUE): Some items were negatively correlated with total scale and were automatically reversed.
##  This is indicated by a negative sign for the variable name.
aocq
## 
## Reliability analysis   
## Call: alpha(x = dat[, 1:18], check.keys = TRUE)
## 
##   raw_alpha std.alpha G6(smc) average_r S/N    ase mean   sd median_r
##       0.89       0.9    0.92      0.33 8.9 0.0082  4.2 0.59     0.33
## 
##  lower alpha upper     95% confidence boundaries
## 0.88 0.89 0.91 
## 
##  Reliability if an item is dropped:
##      raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## q01       0.89      0.90    0.92      0.34 8.6   0.0084 0.024  0.33
## q02       0.89      0.89    0.92      0.33 8.4   0.0086 0.024  0.33
## q03       0.89      0.89    0.92      0.33 8.4   0.0086 0.025  0.33
## q04       0.89      0.90    0.92      0.34 8.6   0.0085 0.024  0.34
## q05       0.89      0.89    0.92      0.33 8.5   0.0086 0.024  0.33
## q06-      0.89      0.89    0.92      0.33 8.3   0.0086 0.024  0.32
## q07-      0.90      0.90    0.92      0.35 9.1   0.0080 0.021  0.34
## q08       0.89      0.89    0.92      0.33 8.4   0.0085 0.024  0.33
## q09       0.90      0.90    0.93      0.35 9.2   0.0080 0.021  0.34
## q10       0.88      0.89    0.92      0.32 8.0   0.0090 0.023  0.31
## q11       0.89      0.89    0.92      0.32 8.1   0.0089 0.023  0.32
## q12       0.88      0.89    0.91      0.32 8.0   0.0091 0.023  0.31
## q13       0.88      0.89    0.92      0.32 8.0   0.0090 0.024  0.31
## q14       0.89      0.89    0.92      0.33 8.4   0.0085 0.022  0.32
## q15       0.89      0.89    0.92      0.33 8.3   0.0086 0.023  0.32
## q16       0.89      0.89    0.92      0.33 8.3   0.0087 0.022  0.32
## q17       0.89      0.89    0.92      0.33 8.4   0.0085 0.021  0.32
## q18       0.88      0.89    0.91      0.32 7.9   0.0090 0.022  0.32
## 
##  Item statistics 
##        n raw.r std.r r.cor r.drop mean   sd
## q01  348  0.57  0.54  0.51   0.48  4.1 1.14
## q02  348  0.63  0.61  0.59   0.55  4.2 1.13
## q03  348  0.61  0.59  0.56   0.53  4.2 1.18
## q04  348  0.54  0.53  0.49   0.48  4.6 0.83
## q05  348  0.60  0.57  0.55   0.53  4.2 1.00
## q06- 348  0.59  0.62  0.58   0.55  4.4 0.72
## q07- 348  0.41  0.38  0.33   0.32  3.8 1.10
## q08  348  0.58  0.59  0.56   0.51  4.3 0.99
## q09  348  0.36  0.36  0.30   0.28  3.4 1.03
## q10  348  0.73  0.74  0.73   0.68  4.0 0.97
## q11  348  0.70  0.71  0.70   0.65  4.3 0.85
## q12  348  0.75  0.74  0.74   0.70  3.9 1.08
## q13  348  0.72  0.72  0.70   0.67  3.9 1.06
## q14  348  0.57  0.59  0.56   0.50  4.2 1.05
## q15  348  0.60  0.63  0.61   0.56  4.5 0.74
## q16  348  0.62  0.64  0.62   0.56  4.3 0.92
## q17  348  0.57  0.60  0.58   0.52  4.4 0.75
## q18  348  0.74  0.75  0.75   0.70  4.1 0.94
## 
## Non missing response frequency for each item
##        1    2    3    4    5 miss
## q01 0.02 0.12 0.11 0.25 0.49    0
## q02 0.03 0.10 0.09 0.24 0.55    0
## q03 0.05 0.08 0.06 0.22 0.59    0
## q04 0.01 0.03 0.06 0.17 0.72    0
## q05 0.02 0.09 0.03 0.36 0.50    0
## q06 0.50 0.41 0.06 0.02 0.00    0
## q07 0.25 0.50 0.07 0.14 0.04    0
## q08 0.03 0.04 0.04 0.30 0.58    0
## q09 0.05 0.09 0.45 0.24 0.17    0
## q10 0.01 0.05 0.26 0.27 0.42    0
## q11 0.01 0.04 0.10 0.33 0.53    0
## q12 0.02 0.09 0.25 0.28 0.36    0
## q13 0.03 0.06 0.23 0.32 0.35    0
## q14 0.05 0.02 0.12 0.33 0.48    0
## q15 0.01 0.01 0.05 0.33 0.60    0
## q16 0.01 0.03 0.14 0.29 0.53    0
## q17 0.00 0.02 0.09 0.37 0.51    0
## q18 0.01 0.05 0.18 0.31 0.45    0
str(aocq)
## List of 14
##  $ total        :'data.frame':   1 obs. of  9 variables:
##   ..$ raw_alpha: num 0.894
##   ..$ std.alpha: num 0.899
##   ..$ G6(smc)  : num 0.924
##   ..$ average_r: num 0.33
##   ..$ S/N      : num 8.87
##   ..$ ase      : num 0.00817
##   ..$ mean     : num 4.15
##   ..$ sd       : num 0.588
##   ..$ median_r : num 0.329
##  $ alpha.drop   :'data.frame':   18 obs. of  8 variables:
##   ..$ raw_alpha: num [1:18] 0.891 0.888 0.889 0.891 0.889 ...
##   ..$ std.alpha: num [1:18] 0.896 0.893 0.894 0.896 0.894 ...
##   ..$ G6(smc)  : num [1:18] 0.921 0.918 0.92 0.921 0.919 ...
##   ..$ average_r: num [1:18] 0.335 0.33 0.331 0.336 0.333 ...
##   ..$ S/N      : num [1:18] 8.58 8.36 8.42 8.6 8.47 ...
##   ..$ alpha se : num [1:18] 0.00844 0.00863 0.00856 0.00849 0.00859 ...
##   ..$ var.r    : num [1:18] 0.0236 0.0239 0.0247 0.0241 0.0237 ...
##   ..$ med.r    : num [1:18] 0.333 0.33 0.333 0.336 0.33 ...
##  $ item.stats   :'data.frame':   18 obs. of  7 variables:
##   ..$ n     : num [1:18] 348 348 348 348 348 348 348 348 348 348 ...
##   ..$ raw.r : num [1:18] 0.565 0.626 0.609 0.539 0.597 ...
##   ..$ std.r : num [1:18] 0.541 0.61 0.591 0.532 0.575 ...
##   ..$ r.cor : num [1:18] 0.508 0.591 0.561 0.495 0.549 ...
##   ..$ r.drop: num [1:18] 0.485 0.555 0.531 0.479 0.531 ...
##   ..$ mean  : num [1:18] 4.07 4.17 4.21 4.57 4.24 ...
##   ..$ sd    : num [1:18] 1.142 1.132 1.183 0.827 1.002 ...
##  $ response.freq: num [1:18, 1:6] 0.02299 0.03161 0.05172 0.00862 0.02011 ...
##   ..- attr(*, "dimnames")=List of 2
##   .. ..$ : chr [1:18] "q01" "q02" "q03" "q04" ...
##   .. ..$ : chr [1:6] "1" "2" "3" "4" ...
##  $ keys         : Named num [1:18] 1 1 1 1 1 -1 -1 1 1 1 ...
##   ..- attr(*, "names")= chr [1:18] "q01" "q02" "q03" "q04" ...
##  $ scores       : num [1:348] 4.28 4.28 4.61 4.72 4.67 ...
##  $ nvar         : int 18
##  $ boot.ci      : NULL
##  $ boot         : NULL
##  $ Unidim       :List of 1
##   ..$ Unidim: num 0.741
##  $ var.r        : num 0.023
##  $ Fit          :List of 1
##   ..$ Fit.off: num 0.951
##  $ call         : language alpha(x = dat[, 1:18], check.keys = TRUE)
##  $ title        : NULL
##  - attr(*, "class")= chr [1:2] "psych" "alpha"
dat$aocq <- aocq$scores

We need to know the content of questions. It looks like q06 and q07 need to be inverted. Aside from this, the scale statistics look very good.

Cognitive

  • q01: In general, change would reduce my ability to have control over what happens at work.
  • q02: I usually resist new thoughts and ideas.
  • q03: I do not like change.
  • q04: Change causes my failure.
  • q05: Most workplace changes bother me.
  • q06: I welcome changes

Affective

  • q07: Change is useful for the organization.
  • q08: Most of my colleagues benefit from change.
  • q09: I do everything I can to support the change.
  • q10: Normally, I support new thoughts and ideas.
  • q11: I have found that most of the changes are pleasant.
  • q12: Normally, I have benefited from the change.

4.2.1.1 Cognition

cor(dat[, 1:6])
##            q01        q02        q03        q04        q05        q06
## q01  1.0000000  0.4411644  0.4479557  0.3399310  0.5397167 -0.2608942
## q02  0.4411644  1.0000000  0.4466012  0.5094128  0.5029079 -0.2782739
## q03  0.4479557  0.4466012  1.0000000  0.4937163  0.4830848 -0.3288808
## q04  0.3399310  0.5094128  0.4937163  1.0000000  0.3947097 -0.2702737
## q05  0.5397167  0.5029079  0.4830848  0.3947097  1.0000000 -0.2865384
## q06 -0.2608942 -0.2782739 -0.3288808 -0.2702737 -0.2865384  1.0000000
cog <- psych::alpha(dat[, 1:6], check.keys=TRUE)
## Warning in psych::alpha(dat[, 1:6], check.keys = TRUE): Some items were negatively correlated with total scale and were automatically reversed.
##  This is indicated by a negative sign for the variable name.
cog
## 
## Reliability analysis   
## Call: psych::alpha(x = dat[, 1:6], check.keys = TRUE)
## 
##   raw_alpha std.alpha G6(smc) average_r S/N   ase mean   sd median_r
##        0.8       0.8    0.78       0.4   4 0.016  4.3 0.72     0.44
## 
##  lower alpha upper     95% confidence boundaries
## 0.77 0.8 0.83 
## 
##  Reliability if an item is dropped:
##      raw_alpha std.alpha G6(smc) average_r S/N alpha se  var.r med.r
## q01       0.77      0.77    0.74      0.40 3.3    0.018 0.0100  0.42
## q02       0.76      0.76    0.73      0.38 3.1    0.019 0.0103  0.37
## q03       0.76      0.76    0.73      0.38 3.1    0.019 0.0120  0.37
## q04       0.77      0.77    0.74      0.40 3.4    0.018 0.0106  0.44
## q05       0.75      0.76    0.72      0.38 3.1    0.020 0.0092  0.39
## q06-      0.81      0.81    0.78      0.46 4.3    0.016 0.0035  0.47
## 
##  Item statistics 
##        n raw.r std.r r.cor r.drop mean   sd
## q01  348  0.74  0.71  0.64   0.57  4.1 1.14
## q02  348  0.76  0.75  0.69   0.61  4.2 1.13
## q03  348  0.77  0.75  0.69   0.62  4.2 1.18
## q04  348  0.69  0.71  0.63   0.56  4.6 0.83
## q05  348  0.76  0.75  0.70   0.63  4.2 1.00
## q06- 348  0.52  0.57  0.42   0.38  4.4 0.72
## 
## Non missing response frequency for each item
##        1    2    3    4    5 miss
## q01 0.02 0.12 0.11 0.25 0.49    0
## q02 0.03 0.10 0.09 0.24 0.55    0
## q03 0.05 0.08 0.06 0.22 0.59    0
## q04 0.01 0.03 0.06 0.17 0.72    0
## q05 0.02 0.09 0.03 0.36 0.50    0
## q06 0.50 0.41 0.06 0.02 0.00    0
dat$cog <- cog$scores

Looking good!

4.2.1.2 Affect

cor(dat[, 7:12])
##            q07        q08        q09        q10        q11        q12
## q07  1.0000000 -0.1636948 -0.1813667 -0.2210561 -0.1370611 -0.2133496
## q08 -0.1636948  1.0000000  0.2760084  0.3681659  0.4501460  0.3643560
## q09 -0.1813667  0.2760084  1.0000000  0.1815702  0.1552254  0.2644436
## q10 -0.2210561  0.3681659  0.1815702  1.0000000  0.5469128  0.4214009
## q11 -0.1370611  0.4501460  0.1552254  0.5469128  1.0000000  0.6201053
## q12 -0.2133496  0.3643560  0.2644436  0.4214009  0.6201053  1.0000000
aff <- psych::alpha(dat[, 7:12], check.keys=TRUE)
## Warning in psych::alpha(dat[, 7:12], check.keys = TRUE): Some items were negatively correlated with total scale and were automatically reversed.
##  This is indicated by a negative sign for the variable name.
aff
## 
## Reliability analysis   
## Call: psych::alpha(x = dat[, 7:12], check.keys = TRUE)
## 
##   raw_alpha std.alpha G6(smc) average_r S/N   ase mean   sd median_r
##       0.71      0.72    0.72       0.3 2.6 0.024    4 0.65     0.26
## 
##  lower alpha upper     95% confidence boundaries
## 0.67 0.71 0.76 
## 
##  Reliability if an item is dropped:
##      raw_alpha std.alpha G6(smc) average_r S/N alpha se  var.r med.r
## q07-      0.74      0.74    0.73      0.36 2.9    0.023 0.0227  0.37
## q08       0.67      0.68    0.67      0.29 2.1    0.029 0.0298  0.22
## q09       0.72      0.73    0.72      0.35 2.7    0.024 0.0270  0.37
## q10       0.65      0.66    0.65      0.28 2.0    0.029 0.0240  0.24
## q11       0.64      0.64    0.60      0.27 1.8    0.030 0.0082  0.24
## q12       0.63      0.65    0.63      0.27 1.8    0.031 0.0199  0.20
## 
##  Item statistics 
##        n raw.r std.r r.cor r.drop mean   sd
## q07- 348  0.52  0.49  0.30   0.26  3.8 1.10
## q08  348  0.67  0.67  0.57   0.48  4.3 0.99
## q09  348  0.54  0.53  0.36   0.31  3.4 1.03
## q10  348  0.69  0.70  0.63   0.52  4.0 0.97
## q11  348  0.72  0.75  0.74   0.59  4.3 0.85
## q12  348  0.74  0.74  0.70   0.57  3.9 1.08
## 
## Non missing response frequency for each item
##        1    2    3    4    5 miss
## q07 0.25 0.50 0.07 0.14 0.04    0
## q08 0.03 0.04 0.04 0.30 0.58    0
## q09 0.05 0.09 0.45 0.24 0.17    0
## q10 0.01 0.05 0.26 0.27 0.42    0
## q11 0.01 0.04 0.10 0.33 0.53    0
## q12 0.02 0.09 0.25 0.28 0.36    0
dat$aff <- aff$scores

A bit marginal, but still acceptable.

4.2.1.3 Behavior

beh <- psych::alpha(dat[, 13:18], check.keys=TRUE)
beh
## 
## Reliability analysis   
## Call: psych::alpha(x = dat[, 13:18], check.keys = TRUE)
## 
##   raw_alpha std.alpha G6(smc) average_r S/N   ase mean   sd median_r
##       0.85      0.85    0.85      0.49 5.8 0.013  4.2 0.69     0.51
## 
##  lower alpha upper     95% confidence boundaries
## 0.82 0.85 0.87 
## 
##  Reliability if an item is dropped:
##     raw_alpha std.alpha G6(smc) average_r S/N alpha se  var.r med.r
## q13      0.83      0.84    0.82      0.51 5.2    0.014 0.0054  0.53
## q14      0.83      0.83    0.82      0.50 5.0    0.015 0.0073  0.52
## q15      0.82      0.83    0.81      0.49 4.9    0.015 0.0082  0.51
## q16      0.82      0.82    0.80      0.48 4.7    0.015 0.0043  0.51
## q17      0.83      0.83    0.81      0.50 4.9    0.015 0.0053  0.50
## q18      0.80      0.82    0.79      0.47 4.4    0.016 0.0049  0.47
## 
##  Item statistics 
##       n raw.r std.r r.cor r.drop mean   sd
## q13 348  0.74  0.72  0.63   0.59  3.9 1.06
## q14 348  0.76  0.74  0.67   0.62  4.2 1.05
## q15 348  0.74  0.76  0.69   0.63  4.5 0.74
## q16 348  0.77  0.78  0.73   0.65  4.3 0.92
## q17 348  0.72  0.75  0.69   0.62  4.4 0.75
## q18 348  0.82  0.81  0.77   0.71  4.1 0.94
## 
## Non missing response frequency for each item
##        1    2    3    4    5 miss
## q13 0.03 0.06 0.23 0.32 0.35    0
## q14 0.05 0.02 0.12 0.33 0.48    0
## q15 0.01 0.01 0.05 0.33 0.60    0
## q16 0.01 0.03 0.14 0.29 0.53    0
## q17 0.00 0.02 0.09 0.37 0.51    0
## q18 0.01 0.05 0.18 0.31 0.45    0
dat$beh <- beh$scores

Looking good!

4.2.2 Organizational innovation

inno <- psych::alpha(dat[, 19:26], check.keys=TRUE)
inno
## 
## Reliability analysis   
## Call: psych::alpha(x = dat[, 19:26], check.keys = TRUE)
## 
##   raw_alpha std.alpha G6(smc) average_r S/N   ase mean   sd median_r
##       0.83      0.84    0.85      0.39 5.2 0.014  4.2 0.55     0.44
## 
##  lower alpha upper     95% confidence boundaries
## 0.8 0.83 0.86 
## 
##  Reliability if an item is dropped:
##     raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## q19      0.86      0.86    0.86      0.47 6.2    0.012 0.021  0.49
## q20      0.79      0.80    0.82      0.37 4.1    0.017 0.036  0.35
## q21      0.79      0.80    0.80      0.36 3.9    0.018 0.030  0.35
## q22      0.79      0.80    0.81      0.36 4.0    0.018 0.037  0.32
## q23      0.84      0.84    0.86      0.44 5.4    0.013 0.039  0.49
## q24      0.80      0.81    0.82      0.38 4.3    0.016 0.037  0.35
## q25      0.80      0.81    0.82      0.37 4.2    0.016 0.037  0.35
## q26      0.82      0.82    0.84      0.40 4.7    0.015 0.036  0.35
## 
##  Item statistics 
##       n raw.r std.r r.cor r.drop mean   sd
## q19 348  0.42  0.40  0.27   0.23  3.6 0.90
## q20 348  0.78  0.78  0.76   0.69  4.4 0.84
## q21 348  0.81  0.81  0.82   0.73  4.4 0.84
## q22 348  0.81  0.81  0.80   0.73  4.3 0.79
## q23 348  0.54  0.52  0.40   0.37  3.8 0.89
## q24 348  0.72  0.73  0.69   0.61  4.3 0.75
## q25 348  0.75  0.77  0.74   0.67  4.6 0.65
## q26 348  0.64  0.65  0.59   0.52  4.4 0.80
## 
## Non missing response frequency for each item
##        1    2    3    4    5 miss
## q19 0.02 0.05 0.46 0.30 0.17    0
## q20 0.01 0.04 0.08 0.27 0.60    0
## q21 0.00 0.05 0.09 0.31 0.55    0
## q22 0.00 0.02 0.14 0.35 0.49    0
## q23 0.01 0.05 0.28 0.42 0.24    0
## q24 0.00 0.03 0.09 0.43 0.46    0
## q25 0.00 0.02 0.02 0.28 0.68    0
## q26 0.01 0.02 0.08 0.34 0.54    0
dat$inno <- inno$scores

Looking good!

4.2.3 Organizational staff happiness

hppy <- psych::alpha(dat[, 27:49], check.keys=TRUE)
hppy
## 
## Reliability analysis   
## Call: psych::alpha(x = dat[, 27:49], check.keys = TRUE)
## 
##   raw_alpha std.alpha G6(smc) average_r S/N    ase mean   sd median_r
##       0.94      0.94    0.96       0.4  15 0.0048  3.1 0.72      0.4
## 
##  lower alpha upper     95% confidence boundaries
## 0.93 0.94 0.95 
## 
##  Reliability if an item is dropped:
##     raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## q27      0.94      0.94    0.96      0.41  15   0.0048 0.014  0.41
## q28      0.94      0.94    0.96      0.41  15   0.0049 0.017  0.41
## q29      0.94      0.94    0.96      0.40  15   0.0050 0.017  0.40
## q30      0.94      0.94    0.96      0.40  15   0.0050 0.016  0.40
## q31      0.94      0.94    0.96      0.40  15   0.0050 0.015  0.40
## q32      0.94      0.94    0.96      0.40  15   0.0049 0.016  0.40
## q33      0.94      0.94    0.96      0.40  15   0.0050 0.016  0.40
## q34      0.94      0.94    0.96      0.40  15   0.0050 0.016  0.40
## q35      0.94      0.94    0.96      0.41  15   0.0049 0.016  0.40
## q36      0.93      0.93    0.96      0.39  14   0.0051 0.016  0.39
## q37      0.93      0.93    0.96      0.39  14   0.0051 0.016  0.39
## q38      0.94      0.94    0.96      0.40  15   0.0050 0.015  0.40
## q39      0.93      0.94    0.96      0.40  15   0.0051 0.016  0.39
## q40      0.94      0.94    0.96      0.40  15   0.0050 0.016  0.40
## q41      0.94      0.94    0.96      0.40  15   0.0050 0.016  0.40
## q42      0.93      0.93    0.96      0.40  14   0.0051 0.016  0.39
## q43      0.94      0.94    0.96      0.40  15   0.0050 0.016  0.40
## q44      0.94      0.94    0.96      0.41  15   0.0049 0.016  0.40
## q45      0.94      0.94    0.96      0.41  15   0.0048 0.015  0.41
## q46      0.94      0.94    0.96      0.40  15   0.0050 0.017  0.40
## q47      0.94      0.94    0.96      0.41  15   0.0049 0.016  0.41
## q48      0.94      0.94    0.96      0.40  15   0.0049 0.016  0.40
## q49      0.94      0.94    0.96      0.41  15   0.0049 0.016  0.40
## 
##  Item statistics 
##       n raw.r std.r r.cor r.drop mean   sd
## q27 348  0.52  0.51  0.49   0.46  3.7 1.20
## q28 348  0.61  0.61  0.59   0.57  2.8 1.08
## q29 348  0.65  0.65  0.64   0.61  2.7 1.18
## q30 348  0.65  0.64  0.64   0.61  3.0 1.21
## q31 348  0.69  0.68  0.68   0.65  2.8 1.30
## q32 348  0.63  0.62  0.61   0.59  2.5 1.11
## q33 348  0.70  0.70  0.69   0.67  2.8 1.06
## q34 348  0.66  0.66  0.64   0.62  2.9 1.03
## q35 348  0.60  0.60  0.58   0.55  2.7 1.24
## q36 348  0.78  0.78  0.77   0.75  3.0 1.13
## q37 348  0.78  0.77  0.77   0.75  3.1 1.06
## q38 348  0.67  0.67  0.66   0.63  2.8 1.10
## q39 348  0.74  0.73  0.72   0.71  2.7 1.18
## q40 348  0.68  0.68  0.68   0.64  3.3 1.06
## q41 348  0.67  0.67  0.66   0.63  2.7 1.17
## q42 348  0.77  0.77  0.76   0.74  3.1 1.11
## q43 348  0.68  0.68  0.67   0.64  3.6 1.04
## q44 348  0.55  0.56  0.54   0.51  3.8 0.91
## q45 348  0.53  0.54  0.52   0.48  3.1 1.12
## q46 348  0.66  0.66  0.65   0.62  3.5 1.04
## q47 348  0.60  0.61  0.60   0.56  3.4 0.99
## q48 348  0.62  0.63  0.62   0.58  3.5 0.88
## q49 348  0.61  0.62  0.60   0.57  3.5 0.97
## 
## Non missing response frequency for each item
##        1    2    3    4    5 miss
## q27 0.05 0.15 0.17 0.30 0.34    0
## q28 0.15 0.20 0.43 0.16 0.06    0
## q29 0.22 0.20 0.34 0.18 0.06    0
## q30 0.15 0.22 0.18 0.39 0.06    0
## q31 0.25 0.17 0.22 0.29 0.07    0
## q32 0.16 0.44 0.20 0.12 0.07    0
## q33 0.14 0.18 0.46 0.15 0.07    0
## q34 0.12 0.16 0.48 0.18 0.06    0
## q35 0.18 0.32 0.19 0.22 0.09    0
## q36 0.11 0.18 0.38 0.22 0.11    0
## q37 0.09 0.18 0.39 0.25 0.08    0
## q38 0.09 0.43 0.18 0.24 0.06    0
## q39 0.18 0.25 0.32 0.18 0.08    0
## q40 0.07 0.12 0.34 0.34 0.13    0
## q41 0.13 0.38 0.20 0.20 0.09    0
## q42 0.10 0.15 0.39 0.26 0.11    0
## q43 0.03 0.12 0.22 0.43 0.20    0
## q44 0.03 0.05 0.18 0.57 0.17    0
## q45 0.04 0.31 0.26 0.25 0.14    0
## q46 0.02 0.18 0.20 0.43 0.16    0
## q47 0.03 0.18 0.28 0.41 0.11    0
## q48 0.02 0.10 0.35 0.43 0.11    0
## q49 0.05 0.11 0.18 0.57 0.09    0
dat$hppy <- hppy$scores

Looking good!

4.2.3.1 Learning (q27 to q30)

lrn <- psych::alpha(dat[, 27:30], check.keys=TRUE)
lrn
## 
## Reliability analysis   
## Call: psych::alpha(x = dat[, 27:30], check.keys = TRUE)
## 
##   raw_alpha std.alpha G6(smc) average_r S/N   ase mean   sd median_r
##       0.82      0.82    0.79      0.53 4.6 0.016    3 0.94     0.51
## 
##  lower alpha upper     95% confidence boundaries
## 0.79 0.82 0.85 
## 
##  Reliability if an item is dropped:
##     raw_alpha std.alpha G6(smc) average_r S/N alpha se   var.r med.r
## q27      0.80      0.80    0.74      0.56 3.9    0.019 0.01121  0.53
## q28      0.79      0.79    0.73      0.56 3.8    0.019 0.01125  0.50
## q29      0.75      0.75    0.66      0.50 3.0    0.023 0.00028  0.50
## q30      0.76      0.76    0.68      0.51 3.2    0.022 0.00038  0.51
## 
##  Item statistics 
##       n raw.r std.r r.cor r.drop mean  sd
## q27 348  0.78  0.78  0.65   0.59  3.7 1.2
## q28 348  0.77  0.78  0.66   0.60  2.8 1.1
## q29 348  0.84  0.84  0.78   0.70  2.7 1.2
## q30 348  0.83  0.83  0.76   0.68  3.0 1.2
## 
## Non missing response frequency for each item
##        1    2    3    4    5 miss
## q27 0.05 0.15 0.17 0.30 0.34    0
## q28 0.15 0.20 0.43 0.16 0.06    0
## q29 0.22 0.20 0.34 0.18 0.06    0
## q30 0.15 0.22 0.18 0.39 0.06    0
dat$lrn <- lrn$scores

4.2.3.2 Self-openness (q31 to q35)

sop <- psych::alpha(dat[, 31:35], check.keys=TRUE)
sop
## 
## Reliability analysis   
## Call: psych::alpha(x = dat[, 31:35], check.keys = TRUE)
## 
##   raw_alpha std.alpha G6(smc) average_r S/N   ase mean   sd median_r
##       0.83      0.84    0.82       0.5 5.1 0.015  2.7 0.89     0.56
## 
##  lower alpha upper     95% confidence boundaries
## 0.8 0.83 0.86 
## 
##  Reliability if an item is dropped:
##     raw_alpha std.alpha G6(smc) average_r S/N alpha se   var.r med.r
## q31      0.79      0.80    0.76      0.50 3.9    0.018 0.00783  0.50
## q32      0.77      0.79    0.76      0.48 3.7    0.020 0.02092  0.52
## q33      0.77      0.78    0.75      0.47 3.6    0.020 0.02060  0.51
## q34      0.78      0.79    0.77      0.49 3.8    0.019 0.01809  0.50
## q35      0.85      0.85    0.81      0.59 5.7    0.013 0.00062  0.59
## 
##  Item statistics 
##       n raw.r std.r r.cor r.drop mean  sd
## q31 348  0.80  0.79  0.74   0.65  2.8 1.3
## q32 348  0.82  0.82  0.76   0.70  2.5 1.1
## q33 348  0.82  0.82  0.77   0.71  2.8 1.1
## q34 348  0.79  0.80  0.74   0.68  2.9 1.0
## q35 348  0.66  0.65  0.51   0.45  2.7 1.2
## 
## Non missing response frequency for each item
##        1    2    3    4    5 miss
## q31 0.25 0.17 0.22 0.29 0.07    0
## q32 0.16 0.44 0.20 0.12 0.07    0
## q33 0.14 0.18 0.46 0.15 0.07    0
## q34 0.12 0.16 0.48 0.18 0.06    0
## q35 0.18 0.32 0.19 0.22 0.09    0
dat$sop <- sop$scores

4.2.3.3 Participation (q36 to q38)

prt <- psych::alpha(dat[, 36:38], check.keys=TRUE)
prt
## 
## Reliability analysis   
## Call: psych::alpha(x = dat[, 36:38], check.keys = TRUE)
## 
##   raw_alpha std.alpha G6(smc) average_r S/N   ase mean   sd median_r
##       0.87      0.87    0.82      0.68 6.5 0.013    3 0.97     0.65
## 
##  lower alpha upper     95% confidence boundaries
## 0.84 0.87 0.89 
## 
##  Reliability if an item is dropped:
##     raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## q36      0.79      0.79    0.65      0.65 3.7    0.023    NA  0.65
## q37      0.78      0.78    0.64      0.64 3.5    0.024    NA  0.64
## q38      0.86      0.87    0.76      0.76 6.4    0.014    NA  0.76
## 
##  Item statistics 
##       n raw.r std.r r.cor r.drop mean  sd
## q36 348  0.90  0.90  0.84   0.77  3.0 1.1
## q37 348  0.90  0.90  0.84   0.78  3.1 1.1
## q38 348  0.86  0.86  0.73   0.68  2.8 1.1
## 
## Non missing response frequency for each item
##        1    2    3    4    5 miss
## q36 0.11 0.18 0.38 0.22 0.11    0
## q37 0.09 0.18 0.39 0.25 0.08    0
## q38 0.09 0.43 0.18 0.24 0.06    0
dat$prt <- prt$scores

4.2.3.4 Positive thinking (q39 to q42)

pth <- psych::alpha(dat[, 39:42], check.keys=TRUE)
pth
## 
## Reliability analysis   
## Call: psych::alpha(x = dat[, 39:42], check.keys = TRUE)
## 
##   raw_alpha std.alpha G6(smc) average_r S/N   ase mean   sd median_r
##       0.84      0.84    0.81      0.58 5.4 0.014    3 0.93     0.57
## 
##  lower alpha upper     95% confidence boundaries
## 0.82 0.84 0.87 
## 
##  Reliability if an item is dropped:
##     raw_alpha std.alpha G6(smc) average_r S/N alpha se  var.r med.r
## q39      0.81      0.81    0.75      0.59 4.4    0.017 0.0023  0.57
## q40      0.82      0.82    0.76      0.61 4.7    0.016 0.0012  0.60
## q41      0.79      0.79    0.71      0.55 3.7    0.020 0.0031  0.56
## q42      0.78      0.78    0.71      0.55 3.6    0.020 0.0024  0.57
## 
##  Item statistics 
##       n raw.r std.r r.cor r.drop mean  sd
## q39 348  0.82  0.81  0.71   0.65  2.7 1.2
## q40 348  0.78  0.79  0.68   0.63  3.3 1.1
## q41 348  0.85  0.85  0.78   0.72  2.7 1.2
## q42 348  0.85  0.85  0.79   0.72  3.1 1.1
## 
## Non missing response frequency for each item
##        1    2    3    4    5 miss
## q39 0.18 0.25 0.32 0.18 0.08    0
## q40 0.07 0.12 0.34 0.34 0.13    0
## q41 0.13 0.38 0.20 0.20 0.09    0
## q42 0.10 0.15 0.39 0.26 0.11    0
dat$pth <- pth$scores

4.2.3.5 Meaningful work (q43 to q45)

mfw <- psych::alpha(dat[, 43:45], check.keys=TRUE)
mfw
## 
## Reliability analysis   
## Call: psych::alpha(x = dat[, 43:45], check.keys = TRUE)
## 
##   raw_alpha std.alpha G6(smc) average_r S/N   ase mean   sd median_r
##       0.62      0.63    0.57      0.37 1.7 0.036  3.5 0.77     0.34
## 
##  lower alpha upper     95% confidence boundaries
## 0.55 0.62 0.69 
## 
##  Reliability if an item is dropped:
##     raw_alpha std.alpha G6(smc) average_r  S/N alpha se var.r med.r
## q43      0.50      0.51    0.34      0.34 1.02    0.053    NA  0.34
## q44      0.36      0.36    0.22      0.22 0.56    0.069    NA  0.22
## q45      0.70      0.70    0.54      0.54 2.35    0.032    NA  0.54
## 
##  Item statistics 
##       n raw.r std.r r.cor r.drop mean   sd
## q43 348  0.77  0.77  0.61   0.44  3.6 1.04
## q44 348  0.80  0.82  0.71   0.56  3.8 0.91
## q45 348  0.71  0.68  0.39   0.31  3.1 1.12
## 
## Non missing response frequency for each item
##        1    2    3    4    5 miss
## q43 0.03 0.12 0.22 0.43 0.20    0
## q44 0.03 0.05 0.18 0.57 0.17    0
## q45 0.04 0.31 0.26 0.25 0.14    0
dat$mwf <- mfw$scores

4.2.3.6 Interesting work (q46 to q49)

wrk <- psych::alpha(dat[, 46:49], check.keys=TRUE)
wrk
## 
## Reliability analysis   
## Call: psych::alpha(x = dat[, 46:49], check.keys = TRUE)
## 
##   raw_alpha std.alpha G6(smc) average_r S/N   ase mean   sd median_r
##       0.82      0.82    0.78      0.53 4.5 0.015  3.5 0.78     0.51
## 
##  lower alpha upper     95% confidence boundaries
## 0.79 0.82 0.85 
## 
##  Reliability if an item is dropped:
##     raw_alpha std.alpha G6(smc) average_r S/N alpha se  var.r med.r
## q46      0.75      0.75    0.68      0.50 3.0    0.023 0.0121  0.44
## q47      0.73      0.73    0.66      0.48 2.7    0.024 0.0086  0.43
## q48      0.84      0.84    0.78      0.63 5.1    0.015 0.0027  0.62
## q49      0.76      0.76    0.71      0.52 3.2    0.022 0.0221  0.44
## 
##  Item statistics 
##       n raw.r std.r r.cor r.drop mean   sd
## q46 348  0.85  0.84  0.78   0.70  3.5 1.04
## q47 348  0.86  0.85  0.81   0.73  3.4 0.99
## q48 348  0.69  0.71  0.54   0.49  3.5 0.88
## q49 348  0.82  0.82  0.73   0.66  3.5 0.97
## 
## Non missing response frequency for each item
##        1    2    3    4    5 miss
## q46 0.02 0.18 0.20 0.43 0.16    0
## q47 0.03 0.18 0.28 0.41 0.11    0
## q48 0.02 0.10 0.35 0.43 0.11    0
## q49 0.05 0.11 0.18 0.57 0.09    0
dat$wrk <- wrk$scores

4.3 Scale and subscale scores

Often we don’t really need item level information anymore. Here we simple extract the subject information and the scale and subscale scores into the dataframe we are going to use fpr descriptive statistics in reports, figures, and as input to some inferential statistics.

dat_w <- 
  dat |> 
  select(Subj, Gender, experience:wrk) |> 
  mutate(cog_c = cog - 3,
         aff_c = aff - 3,
         beh_c = beh - 3)

From the wide format, we may need to go to the long format.

5 Theoretical question

  1. Does organizational innovation depend on cognitive, affective, and behavioral change attitude?
  2. Does organizational happiness depend on cognitive, affective, and behavioral change attitude?
  3. Are these effects moderated by Gender?

6 Method 1: Multiple regression

6.1 DV: innovation

6.1.1 Inferential statistics

m1_inno <- lm(inno ~ 1 + cog + aff + beh, data=dat_w)
summary(m1_inno)
## 
## Call:
## lm(formula = inno ~ 1 + cog + aff + beh, data = dat_w)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.39986 -0.16262 -0.06299  0.20134  1.00713 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.470126   0.139661  10.526  < 2e-16 ***
## cog          0.132842   0.034787   3.819 0.000159 ***
## aff         -0.005108   0.049171  -0.104 0.917325    
## beh          0.522065   0.040294  12.956  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3631 on 344 degrees of freedom
## Multiple R-squared:  0.5658, Adjusted R-squared:  0.5621 
## F-statistic: 149.4 on 3 and 344 DF,  p-value: < 2.2e-16
contrasts(dat_w$Gender) <-  contr.sum(2)
m2_inno <- lm(inno ~ 1 +  cog + aff + beh + Gender, data=dat_w)
summary(m2_inno)
## 
## Call:
## lm(formula = inno ~ 1 + cog + aff + beh + Gender, data = dat_w)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.38483 -0.17133 -0.05772  0.20396  1.01521 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.466565   0.140051  10.472  < 2e-16 ***
## cog          0.131315   0.034995   3.752 0.000206 ***
## aff         -0.006860   0.049384  -0.139 0.889599    
## beh          0.526663   0.041637  12.649  < 2e-16 ***
## Gender1     -0.009338   0.020932  -0.446 0.655782    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3636 on 343 degrees of freedom
## Multiple R-squared:  0.5661, Adjusted R-squared:  0.561 
## F-statistic: 111.9 on 4 and 343 DF,  p-value: < 2.2e-16
m3_inno <- lm(inno ~ 1 + (cog + aff + beh)*Gender, data=dat_w)
summary(m3_inno)
## 
## Call:
## lm(formula = inno ~ 1 + (cog + aff + beh) * Gender, data = dat_w)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.33394 -0.14249 -0.04941  0.18058  1.07076 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.38404    0.14499   9.545  < 2e-16 ***
## cog          0.15586    0.04145   3.760  0.00020 ***
## aff          0.06356    0.05528   1.150  0.25106    
## beh          0.45118    0.04912   9.185  < 2e-16 ***
## Gender1      0.08460    0.14499   0.583  0.55997    
## cog:Gender1 -0.02056    0.04145  -0.496  0.62020    
## aff:Gender1 -0.14161    0.05528  -2.562  0.01085 *  
## beh:Gender1  0.13431    0.04912   2.734  0.00658 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3603 on 340 degrees of freedom
## Multiple R-squared:  0.5776, Adjusted R-squared:  0.5689 
## F-statistic: 66.43 on 7 and 340 DF,  p-value: < 2.2e-16
anova(m1_inno, m2_inno, m3_inno)
## Analysis of Variance Table
## 
## Model 1: inno ~ 1 + cog + aff + beh
## Model 2: inno ~ 1 + cog + aff + beh + Gender
## Model 3: inno ~ 1 + (cog + aff + beh) * Gender
##   Res.Df    RSS Df Sum of Sq      F  Pr(>F)  
## 1    344 45.364                              
## 2    343 45.338  1   0.02631 0.2027 0.65285  
## 3    340 44.132  3   1.20563 3.0961 0.02703 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

6.1.2 Visualization

# cognition
p_cog <- 
  dat_w |> 
  ggplot(aes(x=cog, y= inno, group=Gender, color=Gender)) +
  geom_jitter() + geom_smooth(method="lm") + 
  scale_color_manual("", values=c("blue", "red")) +
  scale_y_continuous("Rating of organization innovation",  breaks=1:5) +
  scale_x_continuous("Attitude to cognitive change",  breaks=1:5) +
  coord_fixed(ratio=1, xlim=c(1,5.5), ylim=c(1,5.5)) +
  theme_bw()
p_cog
## `geom_smooth()` using formula 'y ~ x'

m3_inno_cog <- lm(inno ~ 1 + cog*Gender, data=dat_w)
summary(m3_inno_cog)
## 
## Call:
## lm(formula = inno ~ 1 + cog * Gender, data = dat_w)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.6008 -0.2956  0.1062  0.2758  1.5324 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2.41522    0.16696  14.466  < 2e-16 ***
## cog          0.41788    0.03843  10.875  < 2e-16 ***
## Gender1      0.61404    0.16696   3.678 0.000273 ***
## cog:Gender1 -0.12565    0.03843  -3.270 0.001185 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4716 on 344 degrees of freedom
## Multiple R-squared:  0.2679, Adjusted R-squared:  0.2615 
## F-statistic: 41.96 on 3 and 344 DF,  p-value: < 2.2e-16
# affect
p_aff <- 
  dat_w |> 
  ggplot(aes(x=aff, y= inno, group=Gender, color=Gender)) +
  geom_jitter() + geom_smooth(method="lm") + 
  scale_color_manual("", values=c("blue", "red")) +
  scale_y_continuous("Rating of organization innovation", breaks=1:5) +
  scale_x_continuous("Attitude to affective change", breaks=1:5) +
  coord_fixed(ratio=1, xlim=c(1,5.5), ylim=c(1,5.5)) +
  theme_bw()
p_aff
## `geom_smooth()` using formula 'y ~ x'

m3_inno_aff <- lm(inno ~ 1 + aff*Gender, data=dat_w)
summary(m3_inno_aff)
## 
## Call:
## lm(formula = inno ~ 1 + aff * Gender, data = dat_w)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.29207 -0.21021  0.07796  0.24665  1.17521 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2.15890    0.15632  13.810  < 2e-16 ***
## aff          0.51979    0.03922  13.253  < 2e-16 ***
## Gender1      0.44844    0.15632   2.869  0.00438 ** 
## aff:Gender1 -0.10165    0.03922  -2.592  0.00995 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4437 on 344 degrees of freedom
## Multiple R-squared:  0.3518, Adjusted R-squared:  0.3462 
## F-statistic: 62.24 on 3 and 344 DF,  p-value: < 2.2e-16
# behavior
p_beh <- 
  dat_w |> 
  ggplot(aes(x=beh, y= inno, group=Gender, color=Gender)) +
  geom_jitter() + geom_smooth(method="lm") + 
  scale_y_continuous("Rating of organization innovation", breaks=1:5) +
  scale_x_continuous("Attitude to behavioral change",  breaks=1:5) +
  scale_color_manual("", values=c("blue", "red")) +
  coord_fixed(ratio=1, xlim=c(1,5.5), ylim=c(1,5.5)) +
  theme_bw()
p_beh
## `geom_smooth()` using formula 'y ~ x'

m3_inno_beh <- lm(inno ~ 1 + beh*Gender, data=dat_w)
summary(m3_inno_beh)
## 
## Call:
## lm(formula = inno ~ 1 + beh * Gender, data = dat_w)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.44848 -0.17197 -0.03942  0.20303  1.06293 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.741954   0.128496  13.556   <2e-16 ***
## beh          0.588567   0.030553  19.264   <2e-16 ***
## Gender1     -0.032244   0.128496  -0.251    0.802    
## beh:Gender1  0.002376   0.030553   0.078    0.938    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3721 on 344 degrees of freedom
## Multiple R-squared:  0.5441, Adjusted R-squared:  0.5401 
## F-statistic: 136.9 on 3 and 344 DF,  p-value: < 2.2e-16

The profile of significant effects in m3_inno does not agree with the zero-order relations of these variables, that is when they are assessed independently of each other. This means when the three IVs are in the model they “interfere” with each other. They generate what is known as a suppressor constellation. Suppressor constellations often suggest that there may be an interaction lurking in the data.

6.2 Model explorations

6.2.1 Visualizations

Let’s look at the three plots at the same time.

dat_l <- 
  dat_w |> 
  pivot_longer(cog:beh, names_to = "Attitude", values_to = "rating") |> 
  select(Subj, Gender, Attitude, rating, inno) |> 
  mutate(Attitude = factor(Attitude, levels=c("cog", "aff", "beh")),
         rating_c = rating - 3)

dat_l |> 
  mutate(Attitude = fct_recode(Attitude, Cognition = "cog", Affect = "aff", Behavior = "beh" ),
         Gender = fct_rev(Gender)) |>
  ggplot(aes(x=rating, y=inno, group=Gender, color=Gender)) +
  geom_jitter() + 
  geom_smooth(method="lm", formula=y ~ 1 + poly(x,1)) +
  facet_grid(. ~ Attitude) +
  scale_x_continuous("Rating",  breaks=1:5) +
  scale_y_continuous("Innovation", breaks=1:5) +
  scale_color_manual("", values=c("red", "blue")) +
  coord_fixed(ratio=2, xlim=c(1, 5.5), ylim=c(1,5.5)) +
  theme_bw() + theme(legend.position=c(0.99, 0.01), legend.justification=c(0.99, 0.01))

Let’s look at scatterplot matrices

dat_w |> 
  ggscatmat(columns = c("inno", "cog", "aff", "beh"), color = "Gender", alpha = 1) + 
  theme(legend.position="top", legend.title=element_blank()) +
  guides(colour = guide_legend(override.aes = list(size=3))) +
  scale_color_manual("", values=c("blue", "red")) + 
  theme_bw() + theme(legend.position = "top")

# an alternative with ellipses
scatterplotMatrix(~  inno + cog + aff + beh  | Gender, data=dat_w, 
                    smooth=FALSE, regLine=FALSE, ellipse=TRUE, legend = FALSE )

6.2.2 Residuals

check_model(m3_inno)

m3b_inno <- lm(inno ~ 1 + (cog_c + aff_c + beh_c)*Gender, data=dat_w)
summary(m3b_inno)
## 
## Call:
## lm(formula = inno ~ 1 + (cog_c + aff_c + beh_c) * Gender, data = dat_w)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.33394 -0.14249 -0.04941  0.18058  1.07076 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    3.395833   0.046616  72.848  < 2e-16 ***
## cog_c          0.155855   0.041453   3.760  0.00020 ***
## aff_c          0.063558   0.055281   1.150  0.25106    
## beh_c          0.451185   0.049120   9.185  < 2e-16 ***
## Gender1        0.001025   0.046616   0.022  0.98247    
## cog_c:Gender1 -0.020561   0.041453  -0.496  0.62020    
## aff_c:Gender1 -0.141611   0.055281  -2.562  0.01085 *  
## beh_c:Gender1  0.134315   0.049120   2.734  0.00658 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3603 on 340 degrees of freedom
## Multiple R-squared:  0.5776, Adjusted R-squared:  0.5689 
## F-statistic: 66.43 on 7 and 340 DF,  p-value: < 2.2e-16
check_model(m3b_inno)

6.2.3 Add interaction terms

m4_inno <- lm(inno ~ 1 + cog_c + aff_c*beh_c, data=dat_w)
summary(m4_inno)
## 
## Call:
## lm(formula = inno ~ 1 + cog_c + aff_c * beh_c, data = dat_w)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.40800 -0.18369 -0.06714  0.18725  1.09594 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.35138    0.05103  65.675  < 2e-16 ***
## cog_c        0.15197    0.03516   4.322 2.03e-05 ***
## aff_c        0.11928    0.06661   1.791   0.0742 .  
## beh_c        0.59727    0.04846  12.326  < 2e-16 ***
## aff_c:beh_c -0.11211    0.04094  -2.738   0.0065 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3598 on 343 degrees of freedom
## Multiple R-squared:  0.5751, Adjusted R-squared:  0.5702 
## F-statistic: 116.1 on 4 and 343 DF,  p-value: < 2.2e-16
anova(m1_inno, m4_inno)
## Analysis of Variance Table
## 
## Model 1: inno ~ 1 + cog + aff + beh
## Model 2: inno ~ 1 + cog_c + aff_c * beh_c
##   Res.Df    RSS Df Sum of Sq      F   Pr(>F)   
## 1    344 45.364                                
## 2    343 44.393  1   0.97046 7.4981 0.006499 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
m5_inno <- lm(inno ~ 1 + cog_c + aff_c*beh_c + aff_c*Gender, 
              data=dat_w)
summary(m5_inno)
## 
## Call:
## lm(formula = inno ~ 1 + cog_c + aff_c * beh_c + aff_c * Gender, 
##     data = dat_w)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.40124 -0.18158 -0.05801  0.19285  1.07915 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    3.35257    0.05122  65.451  < 2e-16 ***
## cog_c          0.14914    0.03558   4.191 3.54e-05 ***
## aff_c          0.11955    0.06723   1.778   0.0763 .  
## beh_c          0.59097    0.05108  11.570  < 2e-16 ***
## Gender1        0.01434    0.03781   0.379   0.7047    
## aff_c:beh_c   -0.10409    0.04278  -2.433   0.0155 *  
## aff_c:Gender1 -0.02078    0.03346  -0.621   0.5349    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3606 on 341 degrees of freedom
## Multiple R-squared:  0.5757, Adjusted R-squared:  0.5682 
## F-statistic: 77.11 on 6 and 341 DF,  p-value: < 2.2e-16
anova(m1_inno, m4_inno, m5_inno)
## Analysis of Variance Table
## 
## Model 1: inno ~ 1 + cog + aff + beh
## Model 2: inno ~ 1 + cog_c + aff_c * beh_c
## Model 3: inno ~ 1 + cog_c + aff_c * beh_c + aff_c * Gender
##   Res.Df    RSS Df Sum of Sq      F   Pr(>F)   
## 1    344 45.364                                
## 2    343 44.393  1   0.97046 7.4642 0.006621 **
## 3    341 44.335  2   0.05847 0.2248 0.798757   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

With the interaction between aff and beh in the model, Gender is no longer significant. Perhaps we have been looking at the wrong model.

6.2.4 Interaction of aff x beh

Let’s visualize the aff x beh interaction.

When two continuous variables interact, one option is to turn one of them into a factor and put it in the group. We convert all of three variables into factors.

There are three options

  • we let the program make groups with approx. equal range: cut_interval()
  • we let the program make groups with approx. equal n’s of obs: cut_number()

Looking at the figure, it seems there are very few values below 3. Let’s got with cut_nunber().

dat_w$CogN = cut_number(dat_w$cog, n=3)
dat_w$AffN = cut_number(dat_w$aff, n=3)
dat_w$BehN = cut_number(dat_w$beh, n=3)
dat_w$BehI = cut_interval(dat_w$beh, n=3)

# checks
dat_w |> group_by(BehN) |> summarise(N=n(), aff_M=mean(aff))
## # A tibble: 3 × 3
##   BehN         N aff_M
##   <fct>    <int> <dbl>
## 1 [1.83,4]   132  3.47
## 2 (4,4.67]   110  3.98
## 3 (4.67,5]   106  4.53
dat_w |> group_by(BehI) |> summarise(N=n(), aff_M=mean(aff))
## # A tibble: 3 × 3
##   BehI            N aff_M
##   <fct>       <int> <dbl>
## 1 [1.83,2.89]    18  2.86
## 2 (2.89,3.94]    86  3.51
## 3 (3.94,5]      244  4.19

And the graph:

dat_w |> 
  ggplot(aes(x=aff, y=inno, group=BehN, color=BehN)) +
  geom_jitter() + geom_smooth(method="lm") + 
  scale_color_manual("Beh Bins", values = c("blue", "orange", "red")) +
  facet_grid(. ~ Gender) +
  theme_bw()
## `geom_smooth()` using formula 'y ~ x'

dat_w |> 
  ggplot(aes(x=beh, y=inno, group=AffN, color=AffN)) +
  geom_jitter() + geom_smooth(method="lm") + 
  scale_color_manual("Aff Bins", values = c("blue", "orange", "red")) +
  facet_grid(. ~ Gender) +
  theme_bw()
## `geom_smooth()` using formula 'y ~ x'

dat_w |> group_by(AffN, Gender) |> summarise(N=n(), aff_M=mean(aff))
## `summarise()` has grouped output by 'AffN'. You can override using the
## `.groups` argument.
## # A tibble: 6 × 4
## # Groups:   AffN [3]
##   AffN        Gender     N aff_M
##   <fct>       <fct>  <int> <dbl>
## 1 [2.33,3.67] male      80  3.25
## 2 [2.33,3.67] female    55  3.33
## 3 (3.67,4.5]  male     103  4.23
## 4 (3.67,4.5]  female    64  4.27
## 5 (4.5,5]     male      36  4.88
## 6 (4.5,5]     female    10  4.8
# other variables?
dat_w |> group_by(BehN, Gender) |> summarise(N=n(), aff_M=mean(aff)) # ok
## `summarise()` has grouped output by 'BehN'. You can override using the
## `.groups` argument.
## # A tibble: 6 × 4
## # Groups:   BehN [3]
##   BehN     Gender     N aff_M
##   <fct>    <fct>  <int> <dbl>
## 1 [1.83,4] male      65  3.45
## 2 [1.83,4] female    67  3.50
## 3 (4,4.67] male      73  3.82
## 4 (4,4.67] female    37  4.29
## 5 (4.67,5] male      81  4.55
## 6 (4.67,5] female    25  4.47
dat_w |> group_by(CogN, Gender) |> summarise(N=n(), aff_M=mean(aff)) # ok
## `summarise()` has grouped output by 'CogN'. You can override using the
## `.groups` argument.
## # A tibble: 6 × 4
## # Groups:   CogN [3]
##   CogN     Gender     N aff_M
##   <fct>    <fct>  <int> <dbl>
## 1 [1.5,4]  male      75  3.49
## 2 [1.5,4]  female    42  3.38
## 3 (4,4.83] male      82  4.05
## 4 (4,4.83] female    51  3.94
## 5 (4.83,5] male      62  4.49
## 6 (4.83,5] female    36  4.50

Solution: Don’t include aff now. Try to understand why male and female responded so differently. Start over.

m6_inno <- lm(inno ~ 1 + cog_c + beh_c, data=dat_w)
summary(m6_inno)
## 
## Call:
## lm(formula = inno ~ 1 + cog_c + beh_c, data = dat_w)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.40134 -0.16247 -0.06155  0.20279  1.00553 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.42000    0.04467  76.553  < 2e-16 ***
## cog_c        0.13112    0.03053   4.295 2.28e-05 ***
## beh_c        0.51949    0.03170  16.390  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3626 on 345 degrees of freedom
## Multiple R-squared:  0.5658, Adjusted R-squared:  0.5633 
## F-statistic: 224.8 on 2 and 345 DF,  p-value: < 2.2e-16
m7_inno <- lm(inno ~ 1 + (cog_c + beh_c)*Gender, data=dat_w)
summary(m7_inno)
## 
## Call:
## lm(formula = inno ~ 1 + (cog_c + beh_c) * Gender, data = dat_w)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.38254 -0.16598 -0.06307  0.19797  1.10276 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    3.401568   0.046743  72.772  < 2e-16 ***
## cog_c          0.166786   0.038808   4.298 2.25e-05 ***
## beh_c          0.490151   0.038492  12.734  < 2e-16 ***
## Gender1        0.006464   0.046743   0.138    0.890    
## cog_c:Gender1 -0.059038   0.038808  -1.521    0.129    
## beh_c:Gender1  0.055485   0.038492   1.441    0.150    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3627 on 342 degrees of freedom
## Multiple R-squared:  0.5695, Adjusted R-squared:  0.5632 
## F-statistic: 90.48 on 5 and 342 DF,  p-value: < 2.2e-16
anova(m6_inno, m7_inno)
## Analysis of Variance Table
## 
## Model 1: inno ~ 1 + cog_c + beh_c
## Model 2: inno ~ 1 + (cog_c + beh_c) * Gender
##   Res.Df    RSS Df Sum of Sq      F Pr(>F)
## 1    345 45.365                           
## 2    342 44.984  3   0.38144 0.9667 0.4086
m8_inno <- lm(inno ~ 1 + cog_c*beh_c, data=dat_w)
summary(m8_inno)
## 
## Call:
## lm(formula = inno ~ 1 + cog_c * beh_c, data = dat_w)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.38626 -0.18688 -0.05642  0.18680  1.08387 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.27753    0.07230  45.333  < 2e-16 ***
## cog_c        0.26862    0.06290   4.271 2.52e-05 ***
## beh_c        0.65478    0.06269  10.444  < 2e-16 ***
## cog_c:beh_c -0.11073    0.04438  -2.495   0.0131 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3599 on 344 degrees of freedom
## Multiple R-squared:  0.5735, Adjusted R-squared:  0.5698 
## F-statistic: 154.2 on 3 and 344 DF,  p-value: < 2.2e-16
anova(m6_inno,  m8_inno)
## Analysis of Variance Table
## 
## Model 1: inno ~ 1 + cog_c + beh_c
## Model 2: inno ~ 1 + cog_c * beh_c
##   Res.Df    RSS Df Sum of Sq     F  Pr(>F)  
## 1    345 45.365                             
## 2    344 44.559  1   0.80621 6.224 0.01307 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
dat_w |> 
  ggplot(aes(x=beh, y=inno, group=CogN, color=CogN)) +
  geom_jitter() + geom_smooth(method="lm") + 
  scale_color_manual("Cog Bins", values = c("blue", "orange", "red")) +
  theme_bw()
## `geom_smooth()` using formula 'y ~ x'

check_model(m8_inno)

check_model(m6_inno)

7 Appendix

This command ensures that somebody at some later time can reproduce your analysis.

sessionInfo()
## R version 4.1.2 (2021-11-01)
## Platform: aarch64-apple-darwin20 (64-bit)
## Running under: macOS Monterey 12.2.1
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.1-arm64/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.1-arm64/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] cowplot_1.1.1      GGally_2.1.2       car_3.0-12         carData_3.0-5     
##  [5] performance_0.8.0  psych_2.1.9        summarytools_1.0.0 forcats_0.5.1     
##  [9] stringr_1.4.0      dplyr_1.0.8        purrr_0.3.4        readr_2.1.2       
## [13] tidyr_1.2.0        tibble_3.1.6       ggplot2_3.3.5      tidyverse_1.3.1   
## 
## loaded via a namespace (and not attached):
##  [1] nlme_3.1-155       matrixStats_0.61.0 fs_1.5.2           bit64_4.0.5       
##  [5] lubridate_1.8.0    insight_0.16.0     RColorBrewer_1.1-2 httr_1.4.2        
##  [9] tools_4.1.2        backports_1.4.1    bslib_0.3.1        utf8_1.2.2        
## [13] R6_2.5.1           mgcv_1.8-39        DBI_1.1.2          colorspace_2.0-3  
## [17] withr_2.5.0        tidyselect_1.1.2   mnormt_2.0.2       bit_4.0.4         
## [21] compiler_4.1.2     cli_3.2.0          rvest_1.0.2        see_0.6.9         
## [25] xml2_1.3.3         bayestestR_0.11.5  labeling_0.4.2     sass_0.4.0        
## [29] scales_1.1.1       checkmate_2.0.0    digest_0.6.29      rmarkdown_2.12    
## [33] base64enc_0.1-3    pkgconfig_2.0.3    htmltools_0.5.2    highr_0.9         
## [37] dbplyr_2.1.1       fastmap_1.1.0      rlang_1.0.2        readxl_1.3.1      
## [41] rstudioapi_0.13    pryr_0.1.5         farver_2.1.0       jquerylib_0.1.4   
## [45] generics_0.1.2     jsonlite_1.8.0     vroom_1.5.7        magrittr_2.0.2    
## [49] rapportools_1.0    patchwork_1.1.1    Matrix_1.4-0       Rcpp_1.0.8        
## [53] munsell_0.5.0      fansi_1.0.2        abind_1.4-5        lifecycle_1.0.1   
## [57] stringi_1.7.6      yaml_2.3.5         MASS_7.3-55        plyr_1.8.6        
## [61] grid_4.1.2         ggrepel_0.9.1      parallel_4.1.2     crayon_1.5.0      
## [65] lattice_0.20-45    splines_4.1.2      haven_2.4.3        pander_0.6.4      
## [69] hms_1.1.1          magick_2.7.3       tmvnsim_1.0-2      knitr_1.37        
## [73] pillar_1.7.0       tcltk_4.1.2        codetools_0.2-18   reprex_2.0.1      
## [77] glue_1.6.2         evaluate_0.15      modelr_0.1.8       vctrs_0.3.8       
## [81] tzdb_0.2.0         cellranger_1.1.0   gtable_0.3.0       datawizard_0.3.0  
## [85] reshape_0.8.8      assertthat_0.2.1   xfun_0.30          broom_0.7.12      
## [89] ellipsis_0.3.2